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Report - PEER - University of California, Berkeley

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Develop HazardFunction for SitePerformStructural AnalysisPerformAnalysis <strong>of</strong>Nonstructural SystemsFormStructural ResponseFunctionsFormNon-Structural ResponseFunctionsFormStructural FragilityFunctionsFormNon-Structural FragilityFunctionsFormStructural LossFunctionsFormNon-Structural LossFunctionsPredictLoss as aFunction <strong>of</strong> DamageFigure 2. Performance assessment process.To illustrate application <strong>of</strong> the process, we focus on the first <strong>of</strong> these two usesand for this discussion, use 1 st mode elastic spectral response acceleration (S a1 ) as ourIM and peak interstory drift at each story level ([δ i ]) as our EDP. For a given groundmotion record, scaled to a specific value <strong>of</strong> S a1 , we can perform a nonlinear timehistory analysis <strong>of</strong> the structure and predict [δ i ]. The values <strong>of</strong> [δ i ] predicted by thisanalysis will depend on several factors including our assumptions as to the structure’smass, stiffness, strength, damping, and hysteretic characteristics as well as thespecifics <strong>of</strong> the ground motion record itself. If a different ground motion record wereselected, but all <strong>of</strong> the modeling parameters left unchanged, we would predictsomewhat different values for [δ i ], and, if we were to repeat this process using severaldifferent records, all scaled to the same S a1 , each, would in general, result insomewhat different [δ i ] predictions. If we believe each <strong>of</strong> these records is equallyrepresentative <strong>of</strong> the particular intensity <strong>of</strong> motion, the result is a random distribution<strong>of</strong> [δ i ] that can result from this particular ground motion intensity. This distributioncan be characterized by a mean or median value and a measure <strong>of</strong> its randomvariation. If this process is repeated for a range <strong>of</strong> ground motion intensity values, itis possible to develop a structural response function that indicates the probabledistribution <strong>of</strong> [δ i ] for different levels <strong>of</strong> ground motion intensity (S a1 ). Figure 3illustrates a structural response function <strong>of</strong> this type for a hypothetical single storystructure, showing the median, 10% and 90% confidence bands for [δ i ] as a function<strong>of</strong> S ai .94

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